Kepler's Laws of Planetary Motion
The silent geometry of the planets
Summary
Between 1609 and 1619 Johannes Kepler discovered three simple laws: (1) the planets trace ellipses around the Sun, not circles; (2) a planet moves faster when it is close to the Sun; (3) the cube of the orbit's size is proportional to the square of its period. These three sentences overturned 2,000 years of belief in circular orbits and opened the way to Newton's law of universal gravitation.
In depth
While analysing Tycho Brahe's 20 years of naked-eye observations of Mars, Kepler noticed that Mars's motion did not fit a circular orbit. The discrepancy was only about 8 arcminutes, but Kepler refused to ignore it. He tried for years and finally arrived at the ellipse. This is one of the turning points of the modern scientific method: observation comes before theory. Together the three laws describe the full geometry and dynamics of an orbit: not just position, but speed too. About 70 years later, Newton proved mathematically that these laws follow naturally from the law of universal gravitation, F = G·m₁·m₂/r².
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